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factor(Module) -- factor a ZZ-module

Synopsis

Description

The ring of M must be ZZ.

In the following example we construct a module with a known (but disguised) factorization.

i1 : f = random(ZZ^6, ZZ^4)

o1 = | 1 8 6 4 |
     | 1 9 9 4 |
     | 4 7 5 7 |
     | 6 5 8 2 |
     | 2 1 8 2 |
     | 4 8 1 3 |

              6        4
o1 : Matrix ZZ  <--- ZZ
i2 : M = subquotient ( f * diagonalMatrix{2,3,8,21}, f * diagonalMatrix{2*11,3*5*13,0,21*5} )

o2 = subquotient (| 2  24 48 84  |, | 22  1560 0 420 |)
                  | 2  27 72 84  |  | 22  1755 0 420 |
                  | 8  21 40 147 |  | 88  1365 0 735 |
                  | 12 15 64 42  |  | 132 975  0 210 |
                  | 4  3  64 42  |  | 44  195  0 210 |
                  | 8  24 8  63  |  | 88  1560 0 315 |

                                 6
o2 : ZZ-module, subquotient of ZZ
i3 : factor M

          ZZ   ZZ    ZZ
o3 = ZZ + -- + -- + ----
           5   11   5*13

o3 : Expression of class Sum